Aqueous dispersions of carbon dots (C-dots) showing size tunable multi-colours in day light are obtained through surface functionalization of multi-walled carbon nanotubes (MWCNTs). The size of the C-dots varies with the functionalization temperature and smaller C-dots are found to be formed, at higher temperatures. The average size of the C-dots synthesized at temperatures of 100 degrees C, 80 degrees C and 60 degrees C lies in the range 6 nm-18 nm, based on transmission electron microscopy (TEM) images. The C-dots synthesized at these temperatures exhibit blue, green and golden yellow colours in day light without being excited by any external source. The structural characterizations using X-ray diffraction, Fourier transform infrared spectroscopy and Raman spectroscopy confirm the presence of a high density of functional groups on the surfaces of the C-dots, giving rise to high aqueous solubility. Compared to the Raman spectrum of the MWCNTs, the spectrum of the C-dots shows a significant increase in the intensity of the defect related D band with respect to that of the crystalline G-band, which indicates the presence of a high concentration of defects and the formation of smaller sp(2) carbon clusters. The synthesized C-dots exhibit size dependent optical absorption and emission characteristics. The intriguing optical properties of these C-dots, which include the multi-colour emission at day light and the excitation wavelength and the pH dependent photoluminescence emission, can be mainly attributed to the formation of sp(2) clusters of different sizes embedded in the sp(3) carbon matrix.